Question

Verify divergence theorem for the function F = 2xzi + yzj + z^2k over the upper half of the sphere x^2 + y^2 + z^2 = a^2.​

Answer 1

Step-by-step explanation:

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Answer 2

Concept:

Divergence occurs when an asset's price moves in the opposite direction from other data or from a technical signal, such an oscillator. Divergence signals that the price trend may be waning and, in extreme situations, may even result in a price reversal.

Given:

Here it is given that the function $F = 2xzi + yzj + z^2k$ over the upper half of the sphere $x^2 + y^2 + z^2 = a^2$.

Find:

We have to verify it.

Solution:

$a) F(x, y, z) = x 3 i + 2xz2 j + 3y 2 z k\\divF = ∂ ∂x(x 3 ) + ∂ ∂y (2xz2 ) + ∂∂z (3y 2 z) = 3x 2 + 3y 2$

Hence we have verified it.

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